Binary variables have two values, either 0 or 1. A Boolean function is an expression formed with binary variables, the two binary operators AND and OR, one unary operator NOT, parentheses and equal sign. The value of a function may be 0 or 1, depending on the values of variables present in the Boolean function or expression. For example, if a Boolean function is expressed algebraically as:
F = AB?C
then the value of F will be 1, when A = 1, B = 0, and C = 1. For other values of A, B, C the value of F is 0.
Boolean functions can also be represented by truth tables. A truth table is the tabular form of the values of a Boolean function according to the all possible values of its variables. For an n number of variables, 2n combinations of 1s and 0s are listed and one column represents function values according to the different combinations. For example, for three variables the Boolean function F = AB + C truth table can be written as below in Figure 2.7
SIMPLIFICATION OF BOOLEAN EXPRESSIONS
When a Boolean expression is implemented with logic gates, each literal in the function is designated as input to the gate. The literal may be a primed or unprimed variable. Minimization of the number of literals and the number of terms leads to less complex circuits as well as less number of gates, which should be a designer’s aim. There are several methods to minimize the Boolean function. Here, simplification or minimization of complex algebraic expressions will be shown with the help of postulates and theorems of Boolean algebra.
المادة المعروضة اعلاه هي مدخل الى المحاضرة المرفوعة بواسطة استاذ(ة) المادة . وقد تبدو لك غير متكاملة . حيث يضع استاذ المادة في بعض الاحيان فقط الجزء الاول من المحاضرة من اجل الاطلاع على ما ستقوم بتحميله لاحقا . في نظام التعليم الالكتروني نوفر هذه الخدمة لكي نبقيك على اطلاع حول محتوى الملف الذي ستقوم بتحميله .
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